Just to help out anyone else who is facing this issue. I finally learned how to get this to work. I went to my settings on amazon and selected the "Silverlight" flash player. Then I installed the "One Click Extension Manager" on Chrome, which is not required but it just makes it easier to determine which one or more extensions are interfering with your being able to play amazon video. Just turn off one extension at a time and re-try playing a movie trailer on amazon until you determine which one it is. The extension that was creating the problem for me was "ScriptSafe".
I've just tried this myself and no, Prime Instant videos does not work on my Toshiba Chromebook. There only seems to be a very limited selection of devices that are compatible with Prime Instant videos. Shame.
Well, it works on my Samsung Chromebook but it pixelates a lot in full screen. I believe because it uses a Flash player now controlled by Google called Pepper that their is no HD. Adobe stopped supporting Flash on anything but Windows and Apple's OS X operating systems. So PC and Mac's have the current versions. Google took over support for Flash because it embeds it in Chrome. I find it hit or miss on quality. If you use Linux you also have limited Flash options other than running Chrome or Firefox which does not use a current Flash player. I know, its very confusing and we can hope that Amazon moves to a HTML5 stream soon which will make the Flash problems go away. Netflix does use HTML5 with Chromebooks as a example of really good video playback when it works correctly. Personally, I find my Samsung a bit under powered for video and tend to use a older Core i3 laptop PC for Flash video.